Question

Evaluate the following: \[{{\left( x+4 \right)}^{2}}\].

Answer 1

Hint: This question is from the topic of algebra. In this question, we will evaluate the term \[{{\left( x+4 \right)}^{2}}\]. In solving this question, we are going to use a foil method. We will first understand about the foil method, after that we will apply this method. After solving the further question, we will get our answer. After that, we will see an alternate method to solve this problem.

Complete step-by-step solution:
Let us solve this question.
In this question, we have asked to evaluate \[{{\left( x+4 \right)}^{2}}\]. Or, we can say that we have to solve the term \[{{\left( x+4 \right)}^{2}}\].
As we will use the foil method here to solve this question, so we will first understand about the foil method.
The foil method says that (a+b)(c+d) can also be written as (ac+ad+bc+bd). Or, we can write in mathematical expression as
\[\left( a+b \right)\left( c+d \right)=ac+ad+bc+bd\]
As we know that the term \[{{\left( x+4 \right)}^{2}}\] can also be written as
\[{{\left( x+4 \right)}^{2}}=\left( x+4 \right)\left( x+4 \right)\]
Now, we will use the foil method in the above equation. We can write the above equation as
\[\Rightarrow {{\left( x+4 \right)}^{2}}=x\times x+x\times 4+4\times x+4\times 4\]
The above can also be written as
\[\Rightarrow {{\left( x+4 \right)}^{2}}={{x}^{2}}+4x+4x+{{4}^{2}}\]
As we know that the square of 4 is 16, so we can write the above equation as
\[\Rightarrow {{\left( x+4 \right)}^{2}}={{x}^{2}}+4x+4x+16\]
The above equation can also be written as
\[\Rightarrow {{\left( x+4 \right)}^{2}}={{x}^{2}}+8x+16\]
Hence, we have solved the term \[{{\left( x+4 \right)}^{2}}\]. The answer we have found is \[{{x}^{2}}+8x+16\].

Note: We should have a proper knowledge in the topic of algebra to solve this type of question easily. We should know the formula of the foil method. The formula for foil method is:
\[\left( a+b \right)\left( c+d \right)=ac+ad+bc+bd\]
We can solve this question by alternate method.
For that, we should know the formula of \[{{\left( a+b \right)}^{2}}\]. The formula is \[{{\left( a+b \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}\]
So, using this formula in the term \[{{\left( x+4 \right)}^{2}}\], we can write
\[{{\left( x+4 \right)}^{2}}={{x}^{2}}+2\times x\times 4+{{4}^{2}}\]
The above equation can also be written as
\[\Rightarrow {{\left( x+4 \right)}^{2}}={{x}^{2}}+8x+16\]
We can have the same answer as we have got in the above. So, we can use this method too to solve this type of question.